A086325 Let u(1)=0, u(2)=1, u(k)=u(k-1)+u(k-2)/(k-2); then a(n)=n!*u(n). (Formerly N0672)

0, 2, 6, 36, 220, 1590, 12978, 118664, 1201464, 13349610, 161530270, 2114578092, 29780308116, 448995414686, 7215997736010, 123153028027920, 2224451568754288, 42395429898611154, 850263899633257014, 17900292623858042420, 394701452356069835340, 9096928711444657157382, 218739785834282892557026

Offset

1,2

References

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 263, Table 7.5.1, row 3.

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 210, Table 3, Three-line Latin rectangles.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Gerzson Kéri, The factorization of compressed Chebyshev polynomials and other polynomials related to multiple-angle formulas, Annales Univ. Sci. Budapest (Hungary, 2022) Sect. Comp., Vol. 53, 93-108.

Formula

a(n) = ceiling(n*n!/e) - (1-(-1)^n)/2.

E.g.f.: x^2*exp(-x)/(1-x)^2. - Vladeta Jovovic, Nov 20 2003

a(n) = n*floor((n!+1)/e). [Gary Detlefs, Jul 13 2010]

a(n) = n * A000166(n). [Joerg Arndt, Jul 09 2012]

G.f.: x*f'(x), where f(x) = 1/(1 + x) + Sum_{k>=1} k^k*x^k/(1 + (k + 1)*x)^(k+1). - Ilya Gutkovskiy, Apr 13 2017

Maple

a:=n->n!*add((-1)^k/k!, k=0..n): seq(a(n)*n, n=1..19); # Zerinvary Lajos, Dec 18 2007
with (combstruct):with (combinat):a:=proc(m) [ZL, {ZL=Set(Cycle(Z, card>=m))}, labeled]; end: ZLL:=a(2):seq(count(ZLL, size=n)*fibonacci(2, n), n=1..19); # Zerinvary Lajos, Jun 11 2008
with (combstruct):a:=proc(m) [ZL, {ZL=Set(Cycle(Z, card>=m))}, labeled]; end: ZLL:=a(2):seq(count(ZLL, size=n)*n, n=1..19); # Zerinvary Lajos, Jun 11 2008

Mathematica

Table[Subfactorial[n]*n, {n, 1, 19}] (* Zerinvary Lajos, Jul 09 2009 *)

Prog

(PARI) a(n) = n*((n! + 1)\exp(1)); \\ Indranil Ghosh, Apr 13 2017

Crossrefs

Cf. A000246, A000274, A000166.

Sequence in context: A152668 A213918 A239889 * A343581 A074424 A002868

Adjacent sequences: A086322 A086323 A086324 * A086326 A086327 A086328

Keyword

nonn

Author

N. J. A. Sloane. This sequence appeared in the 1973 "Handbook", but was then omitted from the database. Resubmitted by Benoit Cloitre, Aug 30 2003. Entry revised by N. J. A. Sloane, Jun 11 2012

Status

approved